Transcript
Ubiquituous Quanta - Università del Salento - Sept. 2013 1
Can Physics contribute to a better understanding of problems in Economics?
Emmanuel Haven School of Management University of Leicester - UK
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Structure Very brief overview of economic theory
milestones Very brief overview of financial
economics and econo-physics milestones (i.e. statistical physics applications)
Brief overview of social science and
quantum physics
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Structure (cont’d) Quantum mechanics and
economics/finance Reasonable promise…but…
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Very brief overview of economic theory milestones Economic theory has known over the last 50
years important new developments In the theory of choice we can distinguish three
important models A first model: we have the celebrated expected
utility model of the 50’s (von Neumann and Morgenstern 1953)
J. von Neumann and O. Morgenstern (1953); Theory of Games and Economic Behavior; Princeton University Press
The von Neumann and Morgenstern model interpret uncertainty as objective
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Very brief overview of economic theory milestones (cont’d) The vNM model (as are others)
accept there exists a given quantification of how likely the various outcomes are of a decision
This is given in the form of a probability distribution
See D. Kreps (1988) Notes on the Theory of Choice, Westview Press, Colorado- Boulder
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Very brief overview of economic theory milestones (cont’d) A second model: the Savage model
(1972) where uncertainty is viewed as subjective
L. J. Savage (1972) ; The Foundations of Statistics, J. Wiley and Sons; New York
There are no objective imposed probabilities
Probabilities are entered on the basis of subjective preferences
None of the uncertainty in Savage is objective (probabilities are completely subjective)
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Very brief overview of economic theory milestones (cont’d) A third model: in the Anscombe-
Aumann model (1963) we have a mixture of objective and subjective probabilities
F. J. Anscombe and R.J. Aumann
(1963); A definition of subjective probability, Annals of Mathematical Statistics 34, 199-205
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Very brief overview of economic theory milestones (cont’d)
At the end of the 80’s and the 90’s further
improvements were to be noticed mainly with the work of Machina (1989) and Gilboa et al. (1995)
M. Machina (1989); Dynamic consistency and non-expected utility models of choice under uncertainty, Journal of Economic Literature 27(4), 1622-1668
I. Gilboa and D. Schmeidler (1995); Case based decision theory, The Quarterly Journal of Economics 110 (3), 605-639
For instance, Gilboa et al. (1995) introduced non-additive probabilities into the theory of risk
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Very brief overview of economic theory milestones (cont’d) Outside the theory of choice we
can also mention: The theory of rational expectations T. Sargent (1986); Rational
expectations and inflation; Harper and Row
The theory of rational beliefs M. Kurz (1994b); On the structure
and diversity of rational beliefs; Economic Theory; 4; 859-876
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Structure
We now consider: Very brief overview of financial
economics and econo-physics milestones
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Very brief overview of finance and econo-physics milestones In financial economics we witness the birth of the
celebrated Black-Scholes (1973) option pricing formula
F. Black and M. Scholes (1973); The pricing of options and corporate liabilities, Journal of Political Economy 81, 637-659
In 1989 we see major improvements on the CAPM
model (Breeden et al. 1989) D. Breeden and M. Gibbons and R. Litzenberger
(1989); Empirical test of the consumption oriented CAPM, The Journal of Finance 44(2), 231-262
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Very brief overview of finance and econo-physics milestones (cont’d) The overwhelming majority of
contributions to economic theory in the last 50 years have occurred from economists and sometimes mathematicians
In the ’80 and 90’s, we can also
see contributions from physicists and scientists of other disciplines
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Very brief overview of finance and econo-physics milestones (cont’d)
Statistical physics made some inroads in using specific
physics concepts in especially behavioural economics
The major protagonist in this area is Professor Eugene Stanley – Boston University.
Some examples of contributions (there are MANY examples)
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Very brief overview of finance and econo-physics milestones (cont’d)
In the area of option pricing, we note the work by Borland (2002)
Her work looked at accommodating option pricing with
probability density functions which are more general than the Log-Normal density function
Borland L. (2002); A theory of non-Gaussian option pricing, Quantitative Finance 2(6), 415-431
Numerous congresses have been organized (especially: Applications of Physics in Financial Analysis
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Structure We now consider: Brief overview of social science
and quantum physics
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Brief overview of financial economics and quantum physics
I. In decision making and psychology:
Andrei Khrennikov (2010). Ubiquitous Quantum
Structure: From Psychology to Finance, Springer-Verlag, Berlin, Heidelberg 2010.
D. Aerts, J. Broekaert, L. Gabora and S. Sozzo (2013);
Quantum Structure and Human Thought, Behavioral and Brain Sciences 36(3), 274-276.
D. Aerts* and J. Broekaert and S. Smets (1999); The Liar paradox in a quantum mechanical perspective, Foundations of Science 4, 156-
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Brief overview of financial economics and quantum physics
Busemeyer* et al. (2006) study a model of human
information processing from quantum mechanical concepts
J. Busemeyer* and Wang Z. and Townsend J.T.
(2006); Quantum dynamics of human decision making, Journal of Mathematical Psychology 50 (3), 220-241
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Brief overview of financial economics and quantum physics
J. Acacio de Barros and Patrick Suppes, "Quantum
mechanics, interference, and the brain," Journal of Mathematical Psychology 53, 306–313 (2009).
Trueblood, J. S., Brown, S. D., Heathcote, A., &
Busemeyer, J. R. (2013). Not just for consumers: Context effects are fundamental to decision making. Psychological Science, 24(6), 901-908.
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Brief overview of financial economics and quantum physics (cont’d)
II. In game theory:
Piotrowski et al. (2003) and Eisert* et al. (1999)
provide for an initiation to quantum games
E. W. Piotrowski and J. Sladkowski (2003); An invitation to quantum game theory, International Journal of Theoretical Physics 42, 1089-
J. Eisert* and M. Wilkens and M. Lewenstein (1999); Quantum games and quantum strategies, Physical Review Letters 83, 3077-3080
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Brief overview of financial economics and quantum physics (cont’d) Arfi* B. (2005); Resolving the trust
predicament: a quantum game theoretic approach. Theory and Decision, 59 (2), 127-174
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Brief overview of financial economics and quantum physics (cont’d) III. In finance and financial economics
Baaquie* (1995) wrote a book on
quantum finance in which option pricing theory is explained from a path-integral point of view
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Brief overview of financial economics and quantum physics (cont’d)
B. Baaquie* (2004); Quantum Finance,
Cambridge University Press, Cambridge
E. Haven and A. Khrennikov (2013); Quantum Social Science, Cambridge University Press, Cambridge
Several articles in popular science magazines: New Scientist
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Brief overview of financial economics and quantum physics (cont’d)
Andrei Khrennikov’s paper: Khrennikov A. Yu. (1999); Classical and
quantum mechanics on information spaces with applications to cognitive, psychological, social and anomalous phenomena; Foundations of Physics; 29; 1065-1098
Olga Choustova’s work applies Bohmian mechanics (a particular interpretation of quantum mechanics) to financial economics
O. A. Choustova, Quantum Bohmian model for financial market, Physica A, 374, 304-314 (2006)
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Brief overview of financial economics and quantum physics (cont’d)
E. Haven (2005a); Analytical solutions to the backward Kolmogorov PDE via an adiabatic approximation to the Schrödinger PDE, Journal of Mathematical Analysis and Applications 311, 439-444
E. Haven (2005b); Pilot-wave theory and
financial option pricing, International Journal of Theoretical Physics 44 (11), 1957-1962
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Brief overview of financial economics and quantum physics (cont’d) Segal (1998) developed work on financial option
pricing in a quantum context W. Segal and I.E. Segal (1998); The Black-
Scholes pricing formula in the quantum context, Proceedings of the National Academy of Sciences of the USA 95, 4072-4075
Bordley* (1998) introduced a generalized
Heisenberg Uncertainty principle
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Brief overview of financial economics and quantum physics (cont’d)
R. F. Bordley* (1998); Quantum mechanical and human violations of compound probability principles: Toward a generalized Heisenberg uncertainty principle, Operations Research 46, 923-926
Shubik* (1999) worked on the basics of quantum economics
M. Shubik* (1999); Quantum economics, uncertainty and the optimal grid size, Economics Letters 64 (3), 277-278
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Brief overview of financial economics and quantum physics (cont’d)
Bagarello* (2006) looks at stock markets from an
operator point of view F. Bagarello* (2006); An operatorial approach to
stock markets, Journal of Physics A 39, 6823-6840.
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Structure of the talk We now consider: Quantum methods in economics
and finance?
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Quantum methods in economics and finance? Probabililty interference in decision
making paradoxes Modelling of information in finance and
economics This has been attempted notably with the
use of Bohmian mechanics How is information playing a special role
in physics?
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Structure We now consider: Reasonable promise….but….
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Reasonable promise…but… What follows now – refers only to economics and
finance (and NOT to the progress made in psychology, biology and decision making of using physics concepts)
There are several hurdles which need still crossing before we can really claim physics contributes to a better understanding of economics
Here are some issues – which – i think are not easy to resolve
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Reasonable promise…but…
Prob. 1: economics works with other tools
and different expectations… Why? A) Economic theory thrives around the use
of measure theoretical concepts. Very FEW graduate students in economics do take courses in PDE’s. Physicists in general are not very hot on using measure theoretical concepts in physics. If i) economic theory is the basis of economics and ii) economic theory is revolving around measure theory, then the future for physics and economics does not bode well. B) Also: assumptions in macroeconomics – are off limits for many econophycists (i.e. they will not agree with the assumptions)
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Reasonable promise…but…
Prob. 2: there is little integration between economics/ financial economics and finance
Why? The use of ‘preference modelling’ has been done away with – squarely – in option pricing theory
This is the ‘bread and butter’ of economics
Given this non-integration – it is no wonder that
physics techniques (which lean closest to option pricing theory) do not enter into economics
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Reasonable promise…but…
Prob. 3: Physical intuition of equivalent economics based principles is sometimes very hard to come by
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Reasonable promise…but…
Prob. 3: Physical intuition of equivalent economics based principles is sometimes very hard to come by
The B/S Hamiltonian is a strange animal…
Euler-Lagrange Equations (within least action) are sometimes very difficult to interpret
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So does physics contribute to a better understanding of economics?
I want to propose two major works in the history
of economics: -the work by Nicolae Georgescu Roegen (a
Harvard economist): which introduced in an implicit way entropy in economics: very few economics students know of him!
-the work by Louis Bachelier (and subsequently the contribution of Paul Samuelson to this work). Bachelier laid the groundwork of using Brownian motion in economics (in a slightly wrong way): very few economics students know of him!
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So does physics contribute to a better understanding of economics?
It pains me to see that in economics proper – the
concepts brought into social science by those two luminaries – have not really penetrated...
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THANK YOU
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